When peripheral flexible toe portions of a grinding disk are deflected by contact with a workpiece, restoring forces tending to straighten the peripheral portion are applied to the disk. The restoring forces have a first component which is proportional to the static flexural stiffness of the disk transverse to the plane of the disk, and a second disk membrane component proportional to the centrifugal forces induced in the plane or membrane of the disk by virtue of rotation. When the second force component is substantially larger than the first component, that is, when operating speeds are relatively high, good workpiece finishes result. However, maintaining this condition of dominant membrane forces requires deliberate effort of a skillful operator of the disk grinder. An important application of the invention is in the field of robotics, where the robot does not inherently have a particular skill level for performing the grinding operation. Where the invention is utilized by a human operator, reduction of the level of required skill is also desirable.